Problem: Solve for $x$ and $y$ using elimination. ${-6x+3y = -36}$ ${-5x+y = -39}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-3$ ${-6x+3y = -36}$ $15x-3y = 117$ Add the top and bottom equations together. $9x = 81$ $\dfrac{9x}{{9}} = \dfrac{81}{{9}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-6x+3y = -36}\thinspace$ to find $y$ ${-6}{(9)}{ + 3y = -36}$ $-54+3y = -36$ $-54{+54} + 3y = -36{+54}$ $3y = 18$ $\dfrac{3y}{{3}} = \dfrac{18}{{3}}$ ${y = 6}$ You can also plug ${x = 9}$ into $\thinspace {-5x+y = -39}\thinspace$ and get the same answer for $y$ : ${-5}{(9)}{ + y = -39}$ ${y = 6}$